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Theorem aistia 27865
Description: Given a is equivalent to T., there exists a proof for a. (Contributed by Jarvin Udandy, 30-Aug-2016.)
Hypothesis
Ref Expression
aistia.1  |-  ( ph  <->  T.  )
Assertion
Ref Expression
aistia  |-  ph

Proof of Theorem aistia
StepHypRef Expression
1 aistia.1 . 2  |-  ( ph  <->  T.  )
2 tbtru 1315 . . . 4  |-  ( ph  <->  (
ph 
<->  T.  ) )
3 bicom 191 . . . . 5  |-  ( (
ph 
<->  ( ph  <->  T.  )
)  <->  ( ( ph  <->  T.  )  <->  ph ) )
43biimpi 186 . . . 4  |-  ( (
ph 
<->  ( ph  <->  T.  )
)  ->  ( ( ph 
<->  T.  )  <->  ph ) )
52, 4ax-mp 8 . . 3  |-  ( (
ph 
<->  T.  )  <->  ph )
65biimpi 186 . 2  |-  ( (
ph 
<->  T.  )  ->  ph )
71, 6ax-mp 8 1  |-  ph
Colors of variables: wff set class
Syntax hints:    <-> wb 176    T. wtru 1307
This theorem is referenced by:  bothtbothsame  27867  aistbistaandb  27878  aistbisfiaxb  27888  aisfbistiaxb  27889  dandysum2p2e4  27943
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-tru 1310
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